Added MATLAB rewrite of the CARNOT optimisation function

Simulink/mpc_simulink/casadi_block.m

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+classdef casadi_block < matlab.System & matlab.system.mixin.Propagates
+    % untitled Add summary here
+    %
+    % This template includes the minimum set of functions required
+    % to define a System object with discrete state.
+
+    properties
+        % Public, tunable properties.
+
+    end
+
+    properties (DiscreteState)
+    end
+
+    properties (Access = private)
+        % Pre-computed constants.
+        casadi_solver
+        x0
+        lbx
+        ubx
+        lbg
+        ubg
+    end
+
+    methods (Access = protected)
+        function num = getNumInputsImpl(~)
+            num = 2;
+        end
+        function num = getNumOutputsImpl(~)
+            num = 1;
+        end
+        function dt1 = getOutputDataTypeImpl(~)
+        	dt1 = 'double';
+        end
+        function dt1 = getInputDataTypeImpl(~)
+        	dt1 = 'double';
+        end
+        function sz1 = getOutputSizeImpl(~)
+        	sz1 = [1,1];
+        end
+        function sz1 = getInputSizeImpl(~)
+        	sz1 = [1,1];
+        end
+        function cp1 = isInputComplexImpl(~)
+        	cp1 = false;
+        end
+        function cp1 = isOutputComplexImpl(~)
+        	cp1 = false;
+        end
+        function fz1 = isInputFixedSizeImpl(~)
+        	fz1 = true;
+        end
+        function fz1 = isOutputFixedSizeImpl(~)
+        	fz1 = true;
+        end
+        function setupImpl(obj,~,~)
+            % Implement tasks that need to be performed only once, 
+            % such as pre-computed constants.
+            
+            import casadi.*
+
+            T = 10; % Time horizon
+            N = 20; % number of control intervals
+
+            % Declare model variables
+            x1 = SX.sym('x1');
+            x2 = SX.sym('x2');
+            x = [x1; x2];
+            u = SX.sym('u');
+
+            % Model equations
+            xdot = [(1-x2^2)*x1 - x2 + u; x1];
+
+            % Objective term
+            L = x1^2 + x2^2 + u^2;
+
+            % Continuous time dynamics
+            f = casadi.Function('f', {x, u}, {xdot, L});
+
+            % Formulate discrete time dynamics
+            % Fixed step Runge-Kutta 4 integrator
+            M = 4; % RK4 steps per interval
+            DT = T/N/M;
+            f = Function('f', {x, u}, {xdot, L});
+            X0 = MX.sym('X0', 2);
+            U = MX.sym('U');
+            X = X0;
+            Q = 0;
+            for j=1:M
+               [k1, k1_q] = f(X, U);
+               [k2, k2_q] = f(X + DT/2 * k1, U);
+               [k3, k3_q] = f(X + DT/2 * k2, U);
+               [k4, k4_q] = f(X + DT * k3, U);
+               X=X+DT/6*(k1 +2*k2 +2*k3 +k4);
+               Q = Q + DT/6*(k1_q + 2*k2_q + 2*k3_q + k4_q);
+            end
+            F = Function('F', {X0, U}, {X, Q}, {'x0','p'}, {'xf', 'qf'});
+
+            % Start with an empty NLP
+            w={};
+            w0 = [];
+            lbw = [];
+            ubw = [];
+            J = 0;
+            g={};
+            lbg = [];
+            ubg = [];
+
+            % "Lift" initial conditions
+            X0 = MX.sym('X0', 2);
+            w = {w{:}, X0};
+            lbw = [lbw; 0; 1];
+            ubw = [ubw; 0; 1];
+            w0 = [w0; 0; 1];
+
+            % Formulate the NLP
+            Xk = X0;
+            for k=0:N-1
+                % New NLP variable for the control
+                Uk = MX.sym(['U_' num2str(k)]);
+                w = {w{:}, Uk};
+                lbw = [lbw; -1];
+                ubw = [ubw;  1];
+                w0 = [w0;  0];
+
+                % Integrate till the end of the interval
+                Fk = F('x0', Xk, 'p', Uk);
+                Xk_end = Fk.xf;
+                J=J+Fk.qf;
+
+                % New NLP variable for state at end of interval
+                Xk = MX.sym(['X_' num2str(k+1)], 2);
+                w = {w{:}, Xk};
+                lbw = [lbw; -0.25; -inf];
+                ubw = [ubw;  inf;  inf];
+                w0 = [w0; 0; 0];
+
+                % Add equality constraint
+                g = {g{:}, Xk_end-Xk};
+                lbg = [lbg; 0; 0];
+                ubg = [ubg; 0; 0];
+            end
+
+            % Create an NLP solver
+            prob = struct('f', J, 'x', vertcat(w{:}), 'g', vertcat(g{:}));
+            options = struct('ipopt',struct('print_level',0),'print_time',false);
+            solver = nlpsol('solver', 'ipopt', prob, options);
+
+            obj.casadi_solver = solver;
+            obj.x0 = w0;
+            obj.lbx = lbw;
+            obj.ubx = ubw;
+            obj.lbg = lbg;
+            obj.ubg = ubg;
+        end
+
+        function u = stepImpl(obj,x,t)
+            disp(t)
+            tic
+            w0 = obj.x0;
+            lbw = obj.lbx;
+            ubw = obj.ubx;
+            solver = obj.casadi_solver;
+            lbw(1:2) = x;
+            ubw(1:2) = x;
+            sol = solver('x0', w0, 'lbx', lbw, 'ubx', ubw,...
+                        'lbg', obj.lbg, 'ubg', obj.ubg);
+  
+            u = full(sol.x(3));
+            toc
+        end
+
+        function resetImpl(obj)
+            % Initialize discrete-state properties.
+        end
+    end
+end